Major additions

The campaign now starts on 14 October 1399 (just after the coronation of Henry IV of England.) You can now play countries that went extinct before 1453 - notably the Byzantine Empire, but also Aydin, Aquileia, Galicia, the Jalayirids, Majapaphit, Achaea, Meissen, Polotsk, and Sukhothai. Tech levels have been changed to accommodate the new timeline.

A new system for national and religious decisions replaces many of the random events in previous versions. Some of these replace special events like uniting a country; others let you get certain advantages if you meet the right preconditions.

Countries now get missions to complete, such as the Ottoman mission to seize Istanbul. You can ignore them with no penalty, but there's usually some good bonuses if you carry them out.

Rebels are a lot more detailed now. Each band of them now has their own cause, such as winning independence for their country or installing a pretender on your nation's throne. If you're feeling really weak, you can even give them what they want. If rebels can hold a country's capital for a while, the country is "broken" and the rebel demands automatically imposed.

The AI is improved a lot... or at least, that's what the developers say. To be fair, it is better at attacking your armies (rather than focusing on sieges) and seems to make fewer really terrible decisions. The missions also help focus it as well. It's also more able to act historically, based on goals set in files for each AI player.

Updated map includes 33 new provinces, mostly in Europe.

Domestic

Provincial decisions are choices you make on a local level. These usually involve some tradeoff, such as giving up a little tax income to reduce revolt risk in a province.

National ideas have been overhauled, with several new ones. All the old NIs have some changed effect and/or different tech requirement.

Slider effects are changed significantly. You also can now change your sliders with no stability hit, though patch 3.1 adds effects for each move which are often harmful. Time between slider changes now increases with the size of your country, though government is still important.

The government types you can choose and their effects, incidentally, have been changed too. Republics now let you elect a new leader every few years, giving you some say over the new ruler's skills.

Tribal governments are even worse - large tribal countries have a nasty secession crisis event when the leader dies, so they don't last too long without modernizing. Incidentally, version 3.1 makes it possible to get out of tribal government to a monarchy by event, though it's quite difficult to pull off for an African or American country.

Missionaries have been changed - now they hang out in a province until it's converted, with a fixed annual chance of success. An active missionary increases revolt risk by quite a bit. Their effectiveness is determined by their funding, via the Missionary Maintenance slider.

The Papal Controller can now call for crusades (giving a bonus to everyone at war with the crusade's target) and excommunicate other Catholic rulers who aren't on good terms with the Church, which causes some prestige and reputation damage and cancels the stability penalty for the attackers sharing your religious group.

No stability hit for declaring war on countries of another religion group. Deus Vult, which gave that benefit previously, is now Unam Sanctum, which now applies to countries in the same religious group.

Economic

Trade goods now follow a supply and demand model. Each good is supplied based on a province's population and factors like it being looted. Demand is controlled by certain factors applied around the world - marketplaces will increase demand for spices, and countries at war will demand more iron.

To make dominating trade a little harder, compete chance now decreases a little with every merchant placed in a CoT. Not that it's too difficult to monopolize all trade as the Netherlands, but it's at least a little harder. The cost of sending merchants is also increased, especially for centers outside your culture group.

Inland CoTs are now less valuable, which helps a little with the AI spamming them everywhere.

Diplomatic

New spy missions: "Infiltrate Administration" to lift fog of war on the country, and "Tarnish Reputation" to damage prestige. 3.1 also adds missions to sponsor patriots, nationalists, and pretenders, who are all rebels friendly to you.

Fabricate claims no longer gives you a core - instead, it gives you a year-long casus belli. Also, it's harder to make cores—you must own a conquered province for 50 years to get a core. Getting cores via missions and decisions can be very important.

Revamped Holy Roman Empire. Emperor has an automatic guarantee on all members, in addition to his large manpower and prestige bonuses. Electors will now decide who to vote for based on diplomacy - and in 3.1, this even works some of the time! Humans can also become an elector via event, though I'm not sure it has any diplomatic effects on other member states.

Colonial/naval

Colonies now grow quickly on their own, under good conditions. Growth is affected by a Colonial Maintenance slider, as well as National Ideas, sliders, etc. You still need colonists to found one, and can send more colonists to increase the size of your colony.

Only cores count for the purpose of determining colonial range. This means western European countries have an even greater advantage in colonizing the New World first.

Uncolonized territories now produce an "unknown" trade good. Once you've had a colony established, an event will occur to cause some good to be produced there. See Regions and Colonial Trade Goods.

Tariffs now constitute nearly all income from overseas cities. They take into account tax and production income from your provinces, but also depend on having a large navy - you'll lose some income if you don't have at least one big or small ship for every overseas colony you control.

Pirates now pop up all over the place, blockading your ports like it's going out of style. This was really bad in IN 3.0, but the current patch makes it a little better. To counter them, you can now set your navies on patrol routes through sea zones, which decreases their spawning.

Naval attrition is changed. Your ships won't get any attrition for ships in coastal provinces within your naval supply range (based on colonial range). Outside that range, there's a significant attrition penalty for ships in the open sea (not adjacent to any land) and a constantly increasing penalty for ships that haven't stopped at a friendly port in a while.

Army/warfare

War exhaustion mechanics changed: Wars don't give WE automatically anymore, instead it increases based on provinces occupied on your home continent, blockaded home ports, battle losses, attrition losses and war taxes. War Exhaustion now drains unit morale.

Mercenaries nerfed: They no longer reinforce, take time to recruit (25% of normal units) and can be recruited on occupied territory. The mercenary pool consists of 1/2th infantry, 1/3th cavalry and 1/6th artillery. The amount of used mercenaries decreases the chances of getting new mercenaries in your pool. Getting new mercenaries for your pool is also based on prestige. Mercenaries are not affected by discipline.

Toned reinforcements down: Only 50% reinforcement speed at hostile territory when adjacent to a friendly occupied province, only 10% speed at lack of supply line to a friendly occupied city, no reinforcements at all in empty provinces.

Recruiting troops now takes longer in looted and blockaded provinces.

Artillery provides 50% of its defensive values to the front rank if it is in the back.

Zero morale troops in frontlines will be removed during a combat.

A failed assault makes the garrisons recover morale now, and morale recovers for garrisons the same speed as for normal troops (maintenance!).

It is no longer possible to retreat from a battle for the first 5 days. Armies whose morale collapses in the first 5 days and face more than double the amount of enemies will be eliminated.

It is no longer legal to retreat towards a province with at least 5x your own force.